There is a rapid imaging approach termed BRISK, see FIG. 7. FIG. 7 is a schematic of the BRISK sampling scheme. The top row represents the series of k-space data sets, each data set representing the data form one image frame of a time series. The blue pattern represents the sparse sampling scheme of BRISK (in this case resolved over the cardiac cycle). At each cardiac time point, only a fraction of k-space is sampled. Following the acquisition, the sparsely sampled k-space data are temporally interpolated to make a complete k-space matrix for each time frame. In the BRISK approach, the sampling of k-space data over the time is performed in a sparse manner (i.e. the sampling is distributed over the so called k-t domain). Since BRISK was introduced, others have applied k-t sampling approaches, such as KT-BLAST, which employ uniform levels of sparse sampling. A unique feature of BRISK is that several sparse sampling factors are employed, with the lowest factor applied towards the center of k-space and higher factors applied towards the periphery of k-space, FIG. 5. However, simulations were performed to identify that the sudden transitions of sampling rate that occur between k-space regions were, in part, responsible for generation of Gibbs ringing artifacts in the final BRISK image. Gibbs artifacts manifest as repeating edges in images and are related to sudden transitions that occur in the k-space domain, with the most abrupt transition occurring when k-space sampling is terminated. These artifacts are only apparent when very high sparse sampling factors are employed, limiting the effective acceleration of BRISK to a factor of 8. Experimentation showed that when a uniform sparse sampling factor was applied, the images did not suffer from Gibbs ringing but instead suffered from temporal blurring, i.e. dynamic features tended to gradually morph from one form to another. From this analysis, it was determined that the ideal sparse sampling pattern would only produce gradual change in the k-t domain, and from this, the present invention was developed.
In terms of the sampling pattern, KT-BLAST employs a uniform sampling pattern, and employs a different reconstruction technique, which involves the use of “training data”, i.e. data in which the central region of k-space is sampled for 10-20 seconds, either separately from the KT-BLAST acquisition, or interleaved with the KT-BLAST acquisition. BRISK is characterized by a variable sampling scheme, but this sampling scheme has distinct sample rates applied to regions of k-space. In MACH, the variable sampling pattern is applied in a smoothly varying manner.